A 300 g block connected to a light spring for which the force constant is 7.50 N

Question

A 300 g block connected to a light spring for which the force constant is 7.50 N/m is free to oscillate on a horizontal, frictionless surface. The block is displaced 5.00 cm from equilibrium and released from rest as in the rigure (A) Find the period of its motion (B) Determine the maximum speed of the block. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time A block-spring system that begins its motion from rest with the block atx-A at0. In this case, o; therefore, x-d cos SOLVE IT (A) Find the period of its motion Conceptualize Study the figure and imagine the block moving back and forth in simple harmonic motion once it is released. Set up an experimental model in the vertical direction by hanging a heavy object such as a stapler from a strong rubber band Categorize The block is modeled as a particle in simple harmonic motion. We find values from equations developed in this section for the particle in simple harmonic motion model, so we categorize this example as a substitution problem. Use the equation to find the angular frequency of the block-spring system = 7.50 N/m 300 x 10-3 kg = 5.000 rad/s Use the equation to find the period of the system: 2 2 5.000 rad/s = 1.256 (B) Determine the maximum speed of the block Use the equation to find Vmax: Ynax = aA = (5.000 rad/s)(5.00 x 10.2 m) = 1.25 m/s

Explanation / Answer

x= 0.05 cos (5t )

v = - 0.05*5 sin (5t) = -0.25 sin (5t)

a = -0.05*5^2 cos (5t) = -1.25 cos (5t)

Master it : a) 5t+0.12pi = 2pi

t = 1.88pi/5 = 1.181 s

b) 5t+0.12pi = 1.5pi

t = 1.38pi/5 = 0.867 s

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